SOLUTION: a payphone is holding the maximum amount of 500 coins consisting of quarters, dimes and nickels. the number of quarters is twice the amount of dimes. if the value of all the coins

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Question 1087816: a payphone is holding the maximum amount of 500 coins consisting of quarters, dimes and nickels. the number of quarters is twice the amount of dimes. if the value of all the coins is $88.00, how many nickels are in the payphone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +5n+%2B+10d+%2B+25q+=+8800+ ( in cents )
(2) +q+=+2d+
(3) +n+%2B+d+%2B+q+=+500+
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Multiply both sides of (3) by +5+ and
subtract (3) from (1)
(1) +5n+%2B+10d+%2B+25q+=+8800+
(3) +-5n+-+5d+-+5q+=+2500+
------------------------------
+5d+%2B+20q+=+6300+
+d+%2B+4q+=+1260+
Plug (2) into this result
+d+%2B+4%2A2d+=+1260+
+9d+=+1260+
+d+=+140+
and
(2) +q+=+2d+
(2) +q+=+280+
and
(3) +n+%2B+d+%2B+q+=+500+
(3) +n+%2B+140+%2B+280+=+500+
(3) +n+=+500+-+420+
(3) +n+=+80+
There are 80 nickels
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check:
(1) +5n+%2B+10d+%2B+25q+=+8800+
(1) +5%2A80+%2B+10%2A140+%2B+25%2A280+=+8800+
(1) +400+%2B+1400+%2B+7000+=+8800+
(1) +8800+=+8800+
OK